A general formula for the torsional deflection of shafts

✍ Scribed by S.E. Slocum

• Publisher: Elsevier Science
• Year: 1912
• Tongue: English
• Weight: 230 KB
• Volume: 174
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/s0016-0032(12)90796-6

✦ Synopsis

Introductory. In a preyious article, 1 by considering the internal work of deformation, the writer has derived a general formula for the shearing deflection of beams of arbitrary crosssection, either variable or constant. By the same method, a new and simplified proof of the Fraenkel formula for flexural deflection was also obtained in this article, and it was further shown that all the ordinary formulas for either flexural or shearing deflection are special cases of one or other 0'f the above. Practical application of these formulas was then made to the calculation of the deflection of a planer rail for which both. the cross-sectional area and moment of inertia were variable.

The object of the present article is to. complete this work on deflection by deriving a general formula for torsional deflection. Tile usual analysis of torsional deflection, as given by St. Venant. Bach, and others, involves a more extensive knowledge of higher mathematics than possessed by the average engineer. The derivation here given, however, is very brief, and involves no mathematical principle more difficult than elementary integration.